Actually, my opinion on link's terminian counterpart is given in-game.

I think that link's terminian counterpart is the deku-butler's son.

List of characters in The Legend of Zelda: Majora's Mask - Wikipedia, the free encyclopedia

The deku butler says that link reminds him of his son. We can assume that the twisted sprout that tatl points out between hyrule and termina is his son, as he is seen kneeling next to it at the ending credits, right at the end.

He (the son of the deku-butler who's name is not given) is killed by majora's mask just before link enters termina, and link is cursed within his form right before he enters termina. Link takes his place in termina. Link approaches termina - Deku son is killed - Link is cursed with the form of the deku son - link enters termina. Just seems too perfect. He takes his place in termina. Also, the deku shell when elegy of emptiness is played resembles the twisted sprout seen at the beginning so much...well, it's just uncanny.